A Comprehensive Derivative Operational Matrix Scheme with Modified Lucas Wavelets for Transcendental Differential Equations

Here, a numerical derivative operation matrix scheme based on a modified Lucas wavelet basis is presented to arrive at optimum numerical approximation solutions to transcendental differential equations. By utilizing collocation points, a modified Lucas wavelet basis expansion, and a computation derivative operational matrix approach, we convert the specified transcendental differential equations to their algebraic equivalents. Two examples have been presented to demonstrate the reliability and stability of this approach. Comparatively, the recommended approach yields the best approximation solution for transcendental differential equations, based on the results for the given problems.